Confidence Limits for Parameters of a Normal Distribution From Singly Censored Samples, Using Maximum Likelihood

Abstract

Small samples with censored data, when analyzed by large-sample methods, yield confidence intervals that are too short. This article presents tables for exact confidence limits for the parameters of a normal or lognormal distribution, using maximum likelihood (ML) estimates from singly censored samples. The tables, based on Monte Carlo simulation, cover selected sample sizes up to n = 100 with various r ≤ n observed and (n − r) censored observations; r ranges from 2 to n. The exact ML method is compared to large-sample ML and exact best linear unbiased estimation methods. The tables are used in considering sample sizes for designing life tests.

KEY WORDS:

• Tables
• Censored data
• Small-sample results
• Norma1 and lognormal parameters